WarmPrior: Straightening Flow-Matching Policies with Temporal Priors

Sinjae KangChanyoung KimKaixin WangLi ZhaoKimin Lee

article2026arXiv3 citations

Introduces WarmPrior, a temporal source distribution derived from recent action history that straightens probability paths in flow-matching policies to boost robotic manipulation performance across imitation and reinforcement learning.

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Modern robot control increasingly relies on generative models, such as diffusion and flow-matching policies, to translate camera images and sensor data into precise physical movements. Conventionally, these systems generate actions by transforming a completely random, standard normal noise distribution into a sequence of robot actions. However, treating the starting point as pure, stateless noise ignores the continuous and predictable flow of physical motion. This design flaw forces the robot's control policy to reconstruct every motion trajectory from scratch at each step, resulting in curved generation paths, slower computation, and erratic behavioral switching between different task strategies.

The main objective of the article is to demonstrate that replacing standard random noise with a temporally informed starting distribution, termed WarmPrior, significantly enhances the execution performance, computational speed, and learning efficiency of generative robot policies without modifying the underlying neural networks or training losses.

The approach introduces two simple mechanisms to anchor the starting noise distribution to the robot's own recent movement history, combined with a controlled amount of residual noise. The first variant, WarmPrior-Past, anchors the initial noise to the robot's previously executed action. The second, WarmPrior-Preview, trains the model to forecast twice the required action steps and uses its previous future forecast as the starting point for the current step. The authors evaluated this framework across rigorous simulation suites (Robomimic and MimicGen) and physical robot hardware using a Franka robotic arm across diverse manipulation tasks, testing across varying computational budgets and combining the method with reinforcement learning.

The key findings show consistent, broad-based improvements across all tested domains. First, WarmPrior substantially increases robotic task success rates compared to standard noise baselines, with the most pronounced gains occurring on complex, multi-human demonstration tasks and when compute budgets are constrained to single-step inference (for example, improving success rates from 65.9% to 77.8% on a challenging peg-insertion task). Second, WarmPrior-Preview consistently outperforms WarmPrior-Past because future forecasts provide a closer approximation to the target action than simple past-action persistence. Third, the method straightens the learned mathematical transport trajectories by up to 44%, effectively removing the directional ambiguity that normally curves generative flows. Fourth, in reinforcement learning fine-tuning, WarmPrior restricts the agent's exploration space to a 3-times tighter, meaningful region, enabling it to surpass a 95% success rate on the difficult multi-robot transport task for the first time.

These results demonstrate that the starting noise distribution is a highly practical lever for improving robotic systems. Because WarmPrior straightens generation trajectories, it allows robots to operate accurately at minimal inference steps, directly reducing computational latency, hardware costs, and power requirements. It also resolves dangerous oscillations between conflicting strategies during execution by providing smooth temporal continuity. Furthermore, WarmPrior complements existing inference-time smoothing techniques like Real-Time Chunking, as stacking both approaches yields higher success rates than either method alone.

Based on these findings, engineering and product teams building generative robot policies should replace default random Gaussian starting distributions with temporally grounded priors. Teams should prioritize the preview-based variant when planning horizons allow, or use the past-action variant when simplicity is paramount, maintaining moderate noise levels to avoid collapsing into brittle deterministic behaviors. In addition, organizations fine-tuning diffusion-based policies via reinforcement learning should adopt bounded, anchor-centered action spaces to dramatically reduce sample training time.

A key boundary condition of the study is that the noise variance must remain balanced; reducing noise completely to zero degrades the model into a standard regression approach that fails entirely on multimodal tasks. While the findings provide high confidence across multiple benchmark architectures and tabletop manipulation settings, further validation is recommended on highly agile, long-horizon mobile manipulation platforms in unstructured real-world environments before enterprise-wide deployment.

Korea Advanced Institute of Science and Technology Microsoft reinforcement learning robot system robotic arms WarmPrior flow-matching policies temporal priors

arXiv: 2605.13959 sinnnj/warmprior-bc

Paper: Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow, Xingchao Liu et al. (2023). Introduces the Rectified Flow framework and the concept of straightening probability trajectories, which WarmPrior directly builds upon to motivate its temporal prior construction.
Paper: Diffusion policy: Visuomotor policy learning via action diffusion, Cheng Chi et al. (2023). Establishes the foundational paradigm of diffusion- and generative-based visuomotor policies for robotic manipulation that WarmPrior aims to improve.
Paper: π0: A Vision-Language-Action Flow Model for General Robot Control, Kevin Black et al. (2024). Demonstrates flow-matching architectures for continuous action generation in generalist robot control, representing the core policy class adapted by WarmPrior.
Paper: Flow Q-Learning, Seohong Park et al. (2025). Explores generative flow-based policies and behavioral modeling within reinforcement learning pipelines, providing important background for prior-space exploration.
Paper: Matching Normalizing Flows and Probability Paths on Manifolds, Heli Ben-Hamu et al. (2022). Provides fundamental formulations for continuous flow matching and probability path construction essential to understanding trajectory straightening.

Paper: What to Ignore, What to React: Visually Robust RL Fine-Tuning of VLA Models, Yu Peng et al. (2026). Extends reinforcement learning fine-tuning for vision-language-action policies by introducing action-level invariance and sensitivity objectives to handle out-of-distribution visual shifts.
Paper: TwinBrainVLA: Unleashing the Potential of Generalist VLMs for Embodied Tasks via Asymmetric Mixture-of-Transformers, Bin Yu et al. (2026). Applies flow-matching action generation within an asymmetric dual-pathway architecture to mitigate catastrophic forgetting in vision-language-action models.
Paper: Generative Modeling via Drifting, Mingyang Deng et al. (2026). Proposes an alternative single-step generative modeling paradigm using drifting fields that advances real-time sampling efficiency for control and vision tasks.

Cover for WarmPrior: Straightening Flow-Matching Policies with Temporal Priors

Abstract

Generative policies based on diffusion and flow matching have become a dominant paradigm for visuomotor robotic control. We show that replacing the standard Gaussian source distribution with WarmPrior, a simple temporally grounded prior constructed from readily available recent action history, consistently improves success rates on robotic manipulation tasks. We trace this gain to markedly straighter probability paths, echoing the effect of optimal-transport couplings in Rectified Flow. Beyond standard behavior cloning, WarmPrior also reshapes the exploration distribution in prior-space reinforcement learning, improving both sample efficiency and final performance. Collectively, these results identify the source distribution as an important and underexplored design axis in generative robot control.

Topics

reinforcement learning robot system robotic arms gaussian sources

Keywords

WarmPrior flow-matching policies temporal priors flow-matching action head generative policies visuomotor policies optimal-transport couplings stochastic interpolants diffusion policy temporal consistency

1 Introduction
2 Background and Related Work
3 WarmPrior
4 Main Results
4.1 Simulation
4.2 Real-Robot Experiments
5 Understanding and Extending WarmPrior
5.1 WarmPrior Improves SR by Straightening Flow Trajectories
5.2 WarmPrior as a Tunable Source of Temporal Consistency
5.3 WarmPrior Improves Prior-Space RL Efficiency
6 Conclusion
References
A Visualizing Success-Rate Uncertainty with Beta Posteriors
B Why WarmPrior Straightens Flows: A Branching-Cost Analysis
B.1 The branching cost as endpoint ambiguity
B.2 A detailed derivation of the WarmPrior bound
C Training Details
D σ\sigma Ablation
E Comparing WarmPrior with Real-Time Chunking

Knowls

Knowl 1 — WarmPrior Source Distribution Formulation
model/method
In flow-matching policies for robot manipulation, action trajectories are generated by integrating a velocity field that transports samples from a prior distribution $p_0$ to the data distribution $p_{\text{data}}(\cdot \mid o)$ given an observation $o$ . Rather than using an isotropic Gaussian distribution $\mathcal{N}(0, I)$ , WarmPrior constructs a temporally grounded source distribution centered on recent action history.

Let $a_0$ denote the prior sample of dimension $L \times d_a$ , where $L$ is the action prediction horizon and $d_a$ is the per-step action dimension. Given an index set of warm coordinates $\mathcal{W} \subseteq \{0, \dots, L-1\}$ , a cold complement $\mathcal{C} = \{0, \dots, L-1\} \setminus \mathcal{W}$ , a prior mean vector $\mu$ defined on $\mathcal{W}$ , and a residual standard deviation scalar $\sigma > 0$ , the WarmPrior sample is defined coordinate-wise across timestep indices $\tau \in \{0, \dots, L-1\}$ as:

$a_0[\tau] = \begin{cases} \mu_\tau + \sigma \varepsilon_\tau, & \tau \in \mathcal{W}, \\ \varepsilon_\tau, & \tau \in \mathcal{C}, \end{cases} \quad \varepsilon \sim \mathcal{N}(0, I).$

WarmPrior is instantiated in two primary variants:
1. WarmPrior-Past (WP-Past): Predicts a single chunk of $H$ actions ( $L = H$ ) and sets $\mathcal{W} = \{0, \dots, H-1\}$ . During training, for a sample at index $i$ , $\mu_\tau^{\text{Past}} = a^{\text{data}}[i - H + \tau]$ using the preceding $H$ actions from the demonstration buffer (falling back to $\mathcal{W} = \emptyset$ at episode boundaries). At inference, $\mu_\tau^{\text{Past}} = \hat{a}^{\text{prev}}[\tau]$ , the previously executed action chunk (falling back to $\mathcal{W} = \emptyset$ at the initial step). The default noise scale is $\sigma = 0.5$ .
2. WarmPrior-Preview (WP-Preview): Predicts a horizon of $2H$ actions ( $L = 2H$ ) but executes only the first $H$ . The warm set is the first chunk $\mathcal{W} = \{0, \dots, H-1\}$ , while the preview horizon $\mathcal{C} = \{H, \dots, 2H-1\}$ remains cold noise. During training, the ground-truth target acts as the ideal preview proxy: $\mu_\tau^{\text{Preview}} = a_1[\tau]$ for $\tau \in \{0, \dots, H-1\}$ , where $a_1 \in \mathbb{R}^{2H \times d_a}$ . At inference, the prior mean is the second half of the previous prediction: $\mu_\tau^{\text{Preview}} = \hat{a}^{\text{prev}}[H + \tau]$ for $\tau \in \{0, \dots, H-1\}$ (falling back to $\mathcal{W} = \emptyset$ at the first step). The default noise scale is $\sigma = 1.0$ .
Knowl 2 — Training and Inference Algorithm for Flow-Matching Policies with WarmPrior
algorithm
The algorithm specifies training and inference routines for flow-matching robot policies under WarmPrior. The velocity network $v_\theta(t, a_t, o)$ is trained with standard linear flow matching while only altering the initial sample $a_0$ .
Input: Dataset $D$ , linear interpolant coefficients $\alpha(t) = 1-t$ and $\beta(t) = t$ , noise scale $\sigma$ , chunk length $H$ , prediction horizon $L$ ( $L=H$ for Past, $L=2H$ for Preview)
Parameters: Learnable velocity network $v_\theta$
TRAINING:
for each training iteration do
    Sample observation, target action, and buffer index $(o, a_1, i) \sim D$ , with $a_1 \in \mathbb{R}^{L \times d_a}$
    Draw standard Gaussian noise $\varepsilon \sim \mathcal{N}(0, I)$ of shape $L \times d_a$
    Set $a_0 \leftarrow \varepsilon$
    if PAST and $i \ge H$ (within same episode) then
         $a_0 \leftarrow a^{\text{data}}[i-H:i] + \sigma \varepsilon$
    else if PREVIEW then
         $a_0[0:H] \leftarrow a_1[0:H] + \sigma \varepsilon[0:H]$
         $a_0[H:2H] \leftarrow \varepsilon[H:2H]$
    end if
    Sample time $t \sim \mathcal{U}(0, 1)$
    Compute interpolated point $a_t \leftarrow \alpha(t) a_0 + \beta(t) a_1$
    Compute target velocity $\dot{a}_t \leftarrow \dot{\alpha}(t) a_0 + \dot{\beta}(t) a_1 = a_1 - a_0$
    Compute loss $\mathcal{L}(\theta) \leftarrow \|v_\theta(t, a_t, o) - \dot{a}_t\|_2^2$
    Update $\theta$ via gradient step on $\mathcal{L}(\theta)$
end for
INFERENCE:
Initialize previous prediction record $\hat{a}^{\text{prev}} \leftarrow \emptyset$
Reset environment and observe initial observation $o$
while episode not done do
    Draw noise $\varepsilon \sim \mathcal{N}(0, I)$ of shape $L \times d_a$
    Set $a_0 \leftarrow \varepsilon$
    if PAST and $\hat{a}^{\text{prev}} \ne \emptyset$ then
         $a_0 \leftarrow \hat{a}^{\text{prev}} + \sigma \varepsilon$
    else if PREVIEW and $\hat{a}^{\text{prev}} \ne \emptyset$ then
         $a_0[0:H] \leftarrow \hat{a}^{\text{prev}}[H:2H] + \sigma \varepsilon[0:H]$
         $a_0[H:2H] \leftarrow \varepsilon[H:2H]$
    end if
    Generate action chunk $\hat{a} \leftarrow \text{FMSAMPLE}(v_\theta, a_0, o)$ using an ODE integrator
    Execute action chunk $\hat{a}[0:H]$ on the robot and observe new observation $o$
    Update previous prediction $\hat{a}^{\text{prev}} \leftarrow \hat{a}$
end while
In both variants, when no preceding history is available at episode onset or across trajectory boundaries, the method defaults to standard Gaussian initialization ( $a_0 = \varepsilon$ ).
Knowl 3 — Exact Characterization of Flow-Matching Branching Cost
theoretical result
Let $(A_0, A_1) \sim \Pi_o$ denote the conditional joint distribution over prior samples $A_0 \in \mathbb{R}^d$ and target actions $A_1 \in \mathbb{R}^d$ given policy observation $o$ , where $d = H d_a$ . Under the linear interpolant $A_t = (1-t)A_0 + tA_1$ for $t \in [0, 1]$ , the population flow-matching loss for a velocity field $v_t(\cdot, o)$ is:

$\mathcal{L}_o(v) = \int_0^1 \mathbb{E}_{\Pi_o}\left[ \|v_t(A_t, o) - (A_1 - A_0)\|^2_2 \;\middle|\; o \right] dt.$

For each $t \in [0, 1)$ , the unique $L^2$ -minimizer of $\mathcal{L}_o(v)$ is given by the conditional expectation:

$v_t^\star(x, o) = \mathbb{E}[A_1 - A_0 \mid A_t = x, o] = \frac{\mathbb{E}[A_1 \mid A_t = x, o] - x}{1 - t}.$

The irreducible residual flow-matching error, defined as the branching cost $\mathcal{B}(o) := \mathcal{L}_o(v^\star)$ , is exactly the time-integrated conditional variance of the endpoint $A_1$ given the intermediate state $A_t$ :

$\mathcal{B}(o) = \int_0^1 \frac{1}{(1-t)^2} \mathbb{E}\left[ \|A_1 - \mathbb{E}[A_1 \mid A_t, o]\|^2_2 \;\middle|\; o \right] dt.$

This quantity measures the directional ambiguity remaining in $A_1$ after observing $A_t$ . If $A_t$ uniquely determines $A_1$ almost surely, $\mathcal{B}(o) = 0$ , which corresponds to non-branching optimal transport paths.
Knowl 4 — Upper Bound on Warm-Coordinate Branching Cost
theoretical result
Let $P_{\mathcal{W}}$ denote the orthogonal projection matrix onto the subspace of warm coordinates $\mathcal{W}$ of dimension $d_{\mathcal{W}} = \operatorname{tr}(P_{\mathcal{W}})$ , and let $P_{\mathcal{C}} = I - P_{\mathcal{W}}$ be the projection onto the cold coordinates. Suppose the source distribution is structured as:

$A_0 = P_{\mathcal{W}}(\mu + \sigma \Xi) + P_{\mathcal{C}} \Xi, \quad \Xi \sim \mathcal{N}(0, I_d),$

where $\Xi$ is conditionally independent of $(A_1, \mu)$ given observation $o$ . The warm-coordinate branching cost is defined as:

$\mathcal{B}_{\mathcal{W}}(o) := \int_0^1 \frac{1}{(1-t)^2} \mathbb{E}\left[ \|P_{\mathcal{W}} A_1 - \mathbb{E}[P_{\mathcal{W}} A_1 \mid A_t, o]\|^2_2 \;\middle|\; o \right] dt.$

Under this source structure and linear interpolation $A_t = (1-t)A_0 + tA_1$ , the warm-coordinate branching cost satisfies the upper bound:

$\mathcal{B}_{\mathcal{W}}(o) \le \mathbb{E}\left[ \|P_{\mathcal{W}}(A_1 - \mu)\|^2_2 \;\middle|\; o \right] + \sigma^2 d_{\mathcal{W}}.$

The bound decomposes the irreducible curvature into two terms:
1. Mean Mismatch: $\mathbb{E}[\|P_{\mathcal{W}}(A_1 - \mu)\|^2_2 \mid o]$ , which measures how well the prior mean $\mu$ predicts the target action chunk $A_1$ . For WarmPrior-Preview, this corresponds to forecast error $\mathbb{E}[\|E\|^2 \mid o]$ ; for WarmPrior-Past, it corresponds to persistence residual $\mathbb{E}[\|R\|^2 \mid o]$ between consecutive chunks.
2. Gaussian Dispersion: $\sigma^2 d_{\mathcal{W}}$ , which scales with the injected residual variance.

Knowl 5 — Simulation Benchmark Results on Robomimic and MimicGen

data/table

Simulation success rates (%) evaluating the standard Gaussian prior $\mathcal{N}(0, I)$ baseline against WarmPrior-Past (WP-Past) and WarmPrior-Preview (WP-Preview) using the Diffusion Policy (ChiTransformer) backbone with action-chunk length $H = 8$ across numbers of function evaluations $\text{NFE} \in \{9, 3, 1\}$ . Results are averaged over 3 seeds and 200 episodes per seed (top-3 checkpoint average).

	NFE = 9			NFE = 3			NFE = 1
Task	Base	WP-Past	WP-Preview	Base	WP-Past	WP-Preview	Base	WP-Past	WP-Preview
Robomimic — state observation
Square-PH	86.7	88.1	88.1	86.2	88.0	87.9	83.6	86.6	87.3
Square-MH	65.9	69.2	72.7	65.4	73.2	72.9	65.9	70.1	77.8
Transport-PH	34.1	36.2	43.3	39.0	44.0	49.1	36.8	39.8	47.6
Transport-MH	16.3	20.7	24.3	21.3	30.7	30.4	23.3	30.2	34.5
Tool-Hang-PH	79.4	80.6	82.8	72.3	75.1	75.8	77.7	78.2	81.9
Robomimic — image observation
Square-PH	86.9	88.2	88.7	87.7	89.2	89.6	88.7	89.3	89.1
Square-MH	76.1	78.0	77.8	73.8	77.9	77.1	72.4	77.6	75.1
Transport-PH	92.8	94.5	94.3	92.1	93.9	94.9	91.3	93.4	93.7
Transport-MH	74.8	79.7	79.8	73.8	80.0	80.7	74.3	78.6	79.7
Tool-Hang-PH	43.7	45.8	56.3	36.9	38.4	50.7	41.3	38.9	54.0
MimicGen — image observation
Stack	21.4	22.8	31.6	21.3	23.7	30.7	21.3	22.4	28.7
Coffee	26.8	29.6	34.7	23.3	24.1	33.4	16.2	20.4	29.4
Threading	13.8	15.5	20.9	16.3	16.6	22.0	12.5	15.6	18.0

WP-Preview delivers the highest success rates across most domains, with especially pronounced absolute improvements on challenging tasks (e.g., +12.7% on Tool-Hang-PH image at $\text{NFE}=1$ , +11.2% on Transport-MH state at $\text{NFE}=1$ , and +13.2% on MimicGen Coffee at $\text{NFE}=1$ ). Improvements over the baseline are largest under the one-step generation regime ( $\text{NFE}=1$ ).

Knowl 6 — Pathwise Curvature Reduction and Flow Straightening
empirical result
The pathwise curvature of a learned flow policy path $a: [0, 1] \to \mathbb{R}^{H \times d_a}$ parameterized by velocity field $\dot{a}_t = v_\theta(t, a_t, o)$ is measured via the velocity-variance surrogate:

$\kappa(o) = \int_0^1 \|\dot{a}_t - \bar{v}\|^2_2 \, dt, \quad \text{where } \bar{v} = \int_0^1 \dot{a}_t \, dt.$

Evaluating $\kappa(o)$ with an Euler sampler ( $N = 100$ steps) over 2,000 validation observations on Robomimic state-observation tasks yields the following normalized curvature values (where the standard Gaussian prior $\mathcal{N}(0, I)$ baseline is set to 1.000):
- Square-PH: Baseline = 1.000, WP-Past = 0.823, WP-Preview = 0.803
- Square-MH: Baseline = 1.000, WP-Past = 0.705, WP-Preview = 0.559
- Transport-PH: Baseline = 1.000, WP-Past = 0.720, WP-Preview = 0.692
- Transport-MH: Baseline = 1.000, WP-Past = 0.695, WP-Preview = 0.637
- Tool-Hang-PH: Baseline = 1.000, WP-Past = 0.806, WP-Preview = 0.807
WarmPrior substantially reduces the pathwise curvature across all tasks (up to a 44.1% reduction for WP-Preview on Square-MH). The relative magnitude of curvature reduction closely mirrors the task success rate improvements, supporting the premise that straightening probability trajectories improves generative policy performance.
Knowl 7 — Conditioned-Residual Prior-Space Reinforcement Learning
model/method
In prior-space reinforcement learning (such as Diffusion Steering RL / DSRL), an RL policy generates the initial prior sample $a_0$ for a frozen, pretrained generative policy instead of directly predicting action chunk $a_1$ . Applying WarmPrior modifies this setup into a conditioned-residual search problem.

Rather than exploring the entire uninformative prior space $\mathbb{R}^{H \times d_a}$ with action bound $\delta = 1.5$ centered at the origin, the RL action space is restricted to a tight residual $\Delta$ around the WarmPrior mean $\mu$ :

$a_0 = \mu + \Delta, \quad \Delta = \pi_{\text{RL}}(\tilde{o}) \in [-\delta, \delta]^{H \times d_a},$

where the maximum residual magnitude is set to $\delta = 0.5$ (a $3\times$ reduction in action range), and the observation is augmented to $\tilde{o} = [o, \mu]$ to preserve the Markov property.

When fine-tuning DSRL-NA on Robomimic tasks using a frozen flow-matching backbone pretrained for 3,000 epochs:
- On Square, WP-Past and WP-Preview converge faster and exceed a 0.99 success rate, whereas vanilla DSRL-SAC and DSRL-NA baseline plateaus near 0.90.
- On Transport (the most challenging task), WP-Past and WP-Preview achieve $\sim 0.97$ success rate, whereas baseline DSRL-SAC and DSRL-NA fail to exceed 0.90.
Knowl 8 — Temporal Consistency and Single-Step Horizon Performance
empirical result
Generative behavior cloning policies trained with context-free Gaussian priors $\mathcal{N}(0, I)$ suffer from mode switching in multimodal environments: independent sampling at consecutive inferences causes the robot to oscillate erratically between divergent demonstrated trajectories at decision boundaries. WarmPrior resolves mode switching by implicitly biasing each generation toward the local mode basin established by the previous action.

When action chunking is completely removed by setting the chunk length to $H = 1$ (running fresh policy inference at every single environment timestep with $\text{NFE} = 1$ ):
- On Transport-MH (State): The standard $\mathcal{N}(0, I)$ baseline collapses from 23.3% ( $H=8$ ) down to 1.3%, whereas WarmPrior retains high performance (WP-Past reaches $\approx 28\%$ , WP-Preview reaches $\approx 33\%$ ).
- On MimicGen Coffee (Image): Baseline drops to 16.2%, while WarmPrior recovers performance with gains up to $+14.8\%$ .
These results demonstrate that WarmPrior supplies an implicit temporal consistency mechanism that functions even in the absence of explicit action chunking ( $H = 1$ ), allowing per-step re-planning without mode oscillation.
Knowl 9 — Ablation of Residual Noise Scale and Failure of Deterministic Limits
empirical result
Sweeping the prior standard deviation $\sigma \in \{1.5, 1.0, 0.5, 0.3, 0.1, 0.05, 0\}$ on Robomimic Square-MH ( $H = 8, \text{NFE} = 1$ ) reveals a distinct non-monotonic trade-off between trajectory straightness and prior expressiveness:
- Optimal Values: WP-Preview peaks at $\sigma = 1.0$ (success rate 0.778), maintaining performance within 0.06 of its optimum across $\sigma \in [0.3, 1.5]$ . WP-Past peaks at a tighter scale $\sigma = 0.5$ (success rate 0.701), staying within 0.08 of its peak across $\sigma \in [0.3, 1.0]$ .
- Deterministic Collapse ( $\sigma = 0$ ): In the limit $\sigma \to 0$ , the source becomes a deterministic point mass $a_0 = \mu$ , reducing the generative flow model to a deterministic regression mapping $\mu \mapsto a_1$ . In this limit, success rates sharply collapse to $\approx 0.31$ for WP-Preview and $\approx 0.05$ for WP-Past.
Maintaining $\sigma > 0$ provides the residual capacity necessary to accommodate prior prediction errors while preserving multimodal generative modeling.
Knowl 10 — Real-Robot Evaluation and Synergy with Real-Time Chunking
empirical result
WarmPrior was evaluated on physical Franka Research 3 robot setups across two model families:
1. GR00T N1.5 VLA Backbone ( $\text{NFE} = 4$ , 30 teleoperated demonstrations per task) across four manipulation tasks (mean success rate over 3 seeds, 50 trials per seed):
  - Food Waste Disposal: Baseline $\mathcal{N}(0, I) = 0.76$ , WP-Past = 0.90, WP-Preview = 0.87
  - Cup Stacking: Baseline = 0.33, WP-Past = 0.36, WP-Preview = 0.45
  - Block Stacking: Baseline = 0.43, WP-Past = 0.60, WP-Preview = 0.67
  - Cable Insertion: Baseline = 0.15, WP-Past = 0.36, WP-Preview = 0.41
2. Orthogonality to Real-Time Chunking (RTC) on $\pi_{0.5}$ Backbone: On dynamic whole-arm manipulation tasks (Block Throwing and Towel Folding), WarmPrior (training-time prior shaping) was compared against and stacked with RTC (inference-time prefix clamping):
  - Block Throwing: Baseline = 0.32, RTC = 0.57, WarmPrior = 0.48, RTC + WarmPrior = 0.62
  - Towel Folding: Baseline = 0.50, RTC = 0.67, WarmPrior = 0.68, RTC + WarmPrior = 0.82
The combined configuration outperforms both standalone methods, demonstrating that straightening velocity fields at training time and enforcing continuity via prefix clamping at inference time operate through complementary mechanisms.

Coverage note — None was omitted; all key theoretical derivations, algorithmic variants, empirical simulation/real-robot results, ablations, and reinforcement learning extensions from the paper are covered.

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Citation

MLA

Kang, S., et al. “WarmPrior: Straightening Flow-Matching Policies with Temporal Priors”. arXiv, 2026, https://doi.org/10.48550/arxiv.2605.13959.

APA

Kang, S., Kim, C., Wang, K., Zhao, L., & Lee, K. (2026). WarmPrior: Straightening Flow-Matching Policies with Temporal Priors. arXiv. https://doi.org/10.48550/arxiv.2605.13959

Chicago

Kang, S., C. Kim, K. Wang, L. Zhao, and K. Lee. 2026. “WarmPrior: Straightening Flow-Matching Policies with Temporal Priors”. Preprint, ArXiv. https://doi.org/10.48550/arxiv.2605.13959.

Harvard

Kang, S. et al. (2026) “WarmPrior: Straightening Flow-Matching Policies with Temporal Priors”. arXiv. Available at: https://doi.org/10.48550/arxiv.2605.13959.

Vancouver

1. Kang S, Kim C, Wang K, Zhao L, Lee K (2026) WarmPrior: Straightening Flow-Matching Policies with Temporal Priors. https://doi.org/10.48550/arxiv.2605.13959

BibTeX

@misc{https://doi.org/10.48550/arxiv.2605.13959,
  doi = {10.48550/ARXIV.2605.13959},
  url = {https://arxiv.org/abs/2605.13959},
  author = {Kang, Sinjae and Kim, Chanyoung and Wang, Kaixin and Zhao, Li and Lee, Kimin},
  keywords = {Machine Learning (cs.LG), Artificial Intelligence (cs.AI), Robotics (cs.RO), FOS: Computer and information sciences, FOS: Computer and information sciences},
  title = {WarmPrior: Straightening Flow-Matching Policies with Temporal Priors},
  publisher = {arXiv},
  year = {2026},
  copyright = {Creative Commons Attribution 4.0 International}
}

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WarmPrior: Straightening Flow-Matching Policies with Temporal Priors

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Knowls

Knowl 1 — WarmPrior Source Distribution Formulation

Knowl 2 — Training and Inference Algorithm for Flow-Matching Policies with WarmPrior

Knowl 3 — Exact Characterization of Flow-Matching Branching Cost

Knowl 4 — Upper Bound on Warm-Coordinate Branching Cost

Knowl 5 — Simulation Benchmark Results on Robomimic and MimicGen

Knowl 6 — Pathwise Curvature Reduction and Flow Straightening

Knowl 7 — Conditioned-Residual Prior-Space Reinforcement Learning

Knowl 8 — Temporal Consistency and Single-Step Horizon Performance

Knowl 9 — Ablation of Residual Noise Scale and Failure of Deterministic Limits

Knowl 10 — Real-Robot Evaluation and Synergy with Real-Time Chunking

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